# State of Health Estimation of Li-ion Batteries with Regeneration Phenomena: A Similar Rest Time-Based Prognostic Framework

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. PSO Algorithm

#### 2.2. Gaussian Process Model

## 3. The Proposed Framework

#### 3.1. The Regeneration Phenomenon

#### 3.2. Similar Rest Time-Based Prognostics Strategy

Algorithm 1 Extraction of regeneration region sets and regeneration cycle number series |

1: Input: ${\left\{{c}^{\prime}\left(k\right)\right\}}_{k=1}^{w}$; ${\left\{H\left(k\right)\right\}}_{k=1}^{v}$ |

2: for $i=1$ to $w$ do |

3: set $j=1$ |

4: while(${c}^{\prime}\left(i\right)+j\le v$) and ($H\left({c}^{\prime}\left(i\right)+j\right)-H\left({c}^{\prime}\left(i\right)\right)\ge 0$) do |

5: put cycle number ${c}^{\prime}\left(i\right)+j$ into set ${\mathbf{S}}_{i}$ |

6: $j=j+1$ |

7: end while |

8: end for |

9: for $i=1$ to $w-1$ do |

10: for $j=i+1$ to $w$ do |

11: ${\mathbf{S}}_{i}={\mathbf{S}}_{i}-{\mathbf{S}}_{j}$ |

12: end for |

13: $NUM\left(i\right)=\left|{\mathbf{S}}_{i}\right|$ |

14: end for |

15: $NUM\left(w\right)=\left|{\mathbf{S}}_{w}\right|$ |

16: Output: sets ${\mathbf{S}}_{1},{\mathbf{S}}_{2},\cdots ,{\mathbf{S}}_{w}$ (may need) series ${\left\{NUM\left(w\right)\right\}}_{k=1}^{w}$; |

## 4. Case Studies with NASA Data

#### 4.1. Battery Data Set

#### 4.2. Prediction and Comparison

#### 4.3. Prediction with Various Operation Conditions

#### 4.4. Prediction with Two or More Historical Batteries

## 5. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**State of health (SOH) values over time: (

**a**) batteries No. 05, No. 06 and No. 07 with calendar time; (

**b**) batteries No. 05, No. 06 and No. 07 with cycle number; (

**c**) batteries No. 30 and No. 32 with calendar time; (

**d**) batteries No. 30 and No. 32 with cycle number; (

**e**) batteries No. 47 and No. 48 with calendar time; and (

**f**) batteries No. 47 and No. 48 with cycle number.

**Figure 7.**The extraction of regeneration information: (

**a**) current battery (No. 05); and (

**b**) historical battery (No. 07).

**Figure 12.**Prediction results of SOH: (

**a**) battery No. 30 is the current battery and battery No. 32 is the historical battery; (

**b**) battery No. 32 is the current battery and battery No. 30 is the historical battery; (

**c**) battery No. 47 is the current battery and battery No. 48 is the historical battery; and (

**d**) battery No. 48 is the current battery and battery No. 47 is the historical battery.

Battery ID | Temperature (°C) | Discharge Current (A) | End of Discharge Voltage (V) |
---|---|---|---|

No. 05 | 24 | 2 | 2.7 |

No. 06 | 24 | 2 | 2.5 |

No. 07 | 24 | 2 | 2.2 |

No. 30 | 43 | 4 | 2.2 |

No. 32 | 43 | 4 | 2.7 |

No. 47 | 4 | 1 | 2.5 |

No. 48 | 4 | 1 | 2.7 |

Battery No. | 05 | 06 | 07 | |||
---|---|---|---|---|---|---|

Error Criteria | MAPE (%) | RMSE | MAPE (%) | RMSE | MAPE (%) | RMSE |

LGPFR ^{1} | 23.0 | 1.71 | 10.30 | 6.90 | 1.90 | 1.59 |

QGPFR ^{1} | 1.90 | 1.50 | 7.70 | 5.12 | 5.40 | 5.52 |

C-LGPFR ^{1} | 1.60 | 1.36 | 10.20 | 6.86 | 1.70 | 1.73 |

C-QGPFR ^{1} | 2.10 | 1.80 | 29.0 | 20.44 | 2.60 | 2.69 |

SMK-GPR ^{2} | 1.65 | 1.38 | 10.60 | 7.08 | 1.91 | 1.88 |

P-MGPR ^{2} | 1.55 | 1.36 | 2.96 | 2.12 | 1.09 | 1.14 |

SE-MGPR ^{2} | 1.38 | 1.20 | 2.93 | 2.11 | 1.02 | 1.07 |

IPSO-SVR ^{3} | 0.82 | 0.75 | 2.28 | 1.66 | 1.02 | 0.97 |

SRTPF | 0.62 | 0.61 | 1.41 | 1.25 | 0.76 | 0.83 |

Historical Battery No. | F_{2} (%) | MAPE (%) | RMSE |
---|---|---|---|

05 | 0 | 0.30 | 0.28 |

06 | 0.75 | 0.76 | 0.83 |

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**MDPI and ACS Style**

Qin, T.; Zeng, S.; Guo, J.; Skaf, Z.
State of Health Estimation of Li-ion Batteries with Regeneration Phenomena: A Similar Rest Time-Based Prognostic Framework. *Symmetry* **2017**, *9*, 4.
https://doi.org/10.3390/sym9010004

**AMA Style**

Qin T, Zeng S, Guo J, Skaf Z.
State of Health Estimation of Li-ion Batteries with Regeneration Phenomena: A Similar Rest Time-Based Prognostic Framework. *Symmetry*. 2017; 9(1):4.
https://doi.org/10.3390/sym9010004

**Chicago/Turabian Style**

Qin, Taichun, Shengkui Zeng, Jianbin Guo, and Zakwan Skaf.
2017. "State of Health Estimation of Li-ion Batteries with Regeneration Phenomena: A Similar Rest Time-Based Prognostic Framework" *Symmetry* 9, no. 1: 4.
https://doi.org/10.3390/sym9010004